Prime Minister Boris Johnson has said he has made a "genuine attempt to bridge the chasm" in order to get a fresh Brexit deal with the EU.
He told MPs his plan - which would see Northern Ireland stay in the European single market for goods but leave the customs union - were a "compromise".
But Jeremy Corbyn criticised the "unrealistic and damaging proposals".
Irish PM Leo Varadkar said the new plans were welcome, but "fall short in a number of aspects".
Outgoing European Council President Donald Tusk tweeted the EU was "open but still unconvinced" about the plan, and would "stand fully behind Ireland".
The European Commission said there were "problematic points" in the UK's proposal and "further work is needed".
And the main Brexit-focused group at the European Parliament said the plans "in their current form" did not represent a deal MEPs could ratify.
"The proposals do not address the real issues that need to be resolved if the backstop were to be removed," the group added.
But Swedish Prime Minister Stefan Lofven said that, despite "question marks" over the proposals, they represented a "good start for negotiations".
The EU's chief Brexit negotiator, Michel Barnier, has said he will be in a better position to judge possible future negotiations with the UK once he has spoken to his UK counterpart, David Frost.
The UK government hopes to begin a period of intense negotiations with the aim of reaching a final agreement at an EU summit on 17 October.
The prime minister has said the UK will leave the EU on 31 October, with or without a deal.
In the Commons, Mr Johnson appealed to MPs to support his Brexit plan - a change in tone seen from the stormy scene in Parliament last week, as BBC political correspondent Nick Eardley pointed out:
Interesting that PM is using words like "disappointed" in response to opposition leaders slamming his plan.— Nick Eardley (@nickeardleybbc) October 3, 2019
Not making this a big clash and trying to sound more placatory than usual.
Leaving door open for rebels from opposition parties.
"This government has moved, our proposals do represent a compromise and I hope that the House can now come together in the national interest, behind this new deal," Mr Johnson said.
His proposal aims to replace the Irish border "backstop" in the existing withdrawal agreement - which has been rejected three times by MPs.
The backstop is the controversial "insurance policy" that is meant to keep a free-flowing border on the island of Ireland but which critics - including the PM - fear could trap the UK in EU trading rules indefinitely. It has proved to be the sticking point in negotiations.
"I believe this is our chance and their chance to get a deal," Mr Johnson told MPs. But he said the two sides were "some way from a resolution".
Mr Johnson added that the plan would mean there was no need for checks or infrastructure at or near the border between Ireland and Northern Ireland.
But Labour leader Mr Corbyn said: "The current proposals would damage the whole UK economy, the Northern Irish economy especially and would undermine the Good Friday agreement."
He said the proposals "reject any form of customs union, something demanded by every business and industry body in Britain and every trade union".
"They want to ditch EU standards on workers' rights, regulations and consumer standards and engage in a race to the bottom," he said.
The SNP's Westminster leader Ian Blackford said the PM will "never have the consent of Scotland" for his Brexit deal, saying Mr Johnson "doesn't grasp the reality of a workable backstop".
"It is a half-baked plan from (the prime minister's adviser) Dominic Cummings and his Brexit fanatics," Mr Blackford said.
"The proposed deal is dead before it even left the podium of the Tory conference."
What is in the plan?
Under Mr Johnson's proposals, which he calls a "broad landing zone" for a new deal with the EU:
- Northern Ireland would leave the EU's customs union alongside the rest of the UK, at the start of 2021
- But Northern Ireland would, with the consent of politicians in the Northern Ireland Assembly, continue to apply EU legislation relating to agricultural and other products - what he calls an "all-island regulatory zone"
- This arrangement could, in theory, continue indefinitely, but the consent of Northern Ireland's politicians would have to be sought every four years
- Customs checks on goods traded between the UK and EU would be "decentralised", with paperwork submitted electronically and only a "very small number" of physical checks
- These checks should take place away from the border itself, at business premises or at "other points in the supply chain"
The government is also promising a "New Deal for Northern Ireland", with financial commitments to help manage the changes.
Lib Dem leader Jo Swinson said there was "genuine fear" about his proposals at the Northern Ireland border.
She said his plan "has been denounced as the worst of both worlds", asking: "Will the prime minister now go to the Northern Ireland border and listen to the people and communities there or does he not care?"
However, Conservative MPs voiced their support for the proposals.
Brexiteer Sir Bill Cash welcomed the plan and the "indications of progress in these negotiations".
Tory MP Steven Crabb commended Mr Johnson on the "serious intent and effort he is adopting", saying he is "proving many of his doubters wrong".
He said the "constructive tone" of Mr Johnson "stands in stark contrast to the opposition parties [who] continue to set their face against their own voters".
But the proposals will need the agreement of the EU in order to progress.
A European Commission spokesperson said on Thursday: "There are, as we have said, problematic points in the UK's proposal and further work is needed, but that work needs to be done by the UK and not the other way around.
"We would remind you that it's the UK leaving the EU and not the EU leaving the UK.
"And we are doing everything in our power to ensure that that exit is on an orderly basis and we are willing to engage constructively with our counter-parts but we are not going to be the ones left holding the bag, the ball or any other kind of object."
The proposal was welcomed by the DUP but other political parties in Northern Ireland and business groups have dismissed it.
Irish PM Leo Varadkar said he did not understand how the need for tariff checks could be avoided if Northern Ireland leaves the EU's customs union.
As well as raising concerns about the need for customs checks, he also questioned Mr Johnson's plan to give the Northern Ireland Assembly a vote over entering into a "regulatory zone" with the EU.
He said the views of the "whole population of Northern Ireland" should be represented, and no one party should have a "veto" over the idea.
Ireland's deputy PM Simon Coveney said of Boris Johnson's offer, "if that is the final proposal, there will be no deal".
His comments were met with anger from the Democratic Unionist Party, who described them as "quite outrageous".
DUP leader Arlene Foster called for other EU leaders to "prevail upon the Irish government", adding that if the UK's proposals were rejected and it led to a no-deal Brexit "the Irish prime minister is going to be responsible".
She added: "He will go down in history as the man that instituted a hard border on the island of Ireland".
Guy Verhofstadt, chairman of the European Parliament Brexit steering committee, told the BBC's Katya Adler that Parliament was "very sceptical" of Mr Johnson's plan and said it was "not a serious alternative" to the backstop, but rather a "repackaging of old proposals".
Mr Verhofstadt concluded the PMs proposals were ‘absolutely not an alternative to the backstop’. He said it was ‘in the hands of Mr Johnson’ whether/not a new Brexit deal could be struck. If PM presents ‘serious proposals’ says @guyverhofstadt then a new agreement could be made/6— katya adler (@BBCkatyaadler) October 3, 2019